For the nonlinear compression, we utilize a deep convolutional autoencoder. The \({z}_1^{\mathbf {u}}, \cdots , {z}_\mathrm {Q}^{\mathbf {u}}\) , \({z}_1^p, \cdots , {z}_\mathrm {Q}^p\) , and \({z}_1^T, \cdots , {z}_\mathrm {Q}^T\)  represent the nonlinear manifold (also refered to as nonlinear manifolds) of the velocity, pressure, and temperature fields respectively. More details for \(\mathbf {z}\)  will be presented in Section REF . Again, our goal is to achieve \(\mathrm {Q} \ll \mathrm {M} N^t\) . Autoencoders could be considered as a nonlinear variation of POD [1]}, [2]}, [3]} and have been recently used in physics-based modeling [4]}, [5]}, [6]}, [7]}. They use the so-called bottleneck inside their hidden layers to force the networks to identify a reduced representation \(\mathbf {z}\)  of the training examples [3]}, [9]}. We will discuss these linear and nonlinear compression approaches in detail in the following sections.
